The author argues that the idea of canonical elements provides a coherent relationship between equivalence relations, the basis of modern approaches to too many mathematical topics, and the traditional aspect of computation. Examples of equivalent relations, canonical elements, and their calculations are given. (MK)

The historical development of the integers, the rationals, the reals, and the complex numbers is traced. (MK)

An attempt to introduce subtraction of negative integers early in the secondary school curriculum is described. The attempt was not successful, and several aspects of the experiment are discussed. (SD)

The arithmetic needed for complex calculation using an electronic calculator is explained and exemplified. Problems involving square roots, number theory, Fibonacci numbers, and electrical resistances are solved. (SD)

Tests for divisibility in bases 2 through 10 are presented. Two strategies used by a group of fourth-year students are described. (MNS)

Modular arithmetic is used to find the frequency of Friday 13th's in any year. (MM)

After briefly presenting possible origins for the use of the decimal system for counting and the duodecimal (base twelve) system for many measures, a notational scheme using six positive'' digits and six negative'' digits is presented. Examples and algorithms using this set of digits for operations with whole numbers, fractions, and in…

Mathematical concepts and experiences are recalled and organized in a flow chart format. The power of unifying ideas in mathematics often causes this sequence to be forgotten or assigned less importance than it should be. (SD)

Described is mathematics used by the ancient Babylonians and recorded on tablets which have been dated 3000-2000 B.C., and 700-500 B.C. (SD)

Describes number strips, arrow diagrams, and grids for number operations. Provides diagrams for the activity materials. (YP)

Discusses a number series made from the multiplication of numbers to digits. Presents a number series for diverse multiplication numbers. (YP)

Ways in which parents, the media and commercial educational materials contribute to the development of erroneous number concepts in pre-school children are identified. Cautions against these practices are suggested which include the use of more than one set of numerals for representing numbers. (JP)

Number bases other than ten can be introduced effectively by presenting fictional civilizations which use them. (SD)

The system of International Standard Book Numbers uses a check code based on modular arithmetic. This system, the use of a simple machine to compute check digits, and related classroom activities are described. (SD)

The author discusses the impact of mathematical developments around the turn of the century, and historical concerns and development of mathematics education. This article is a continuation of SE 515 504. (SD)